Conventional lithography systems include, among other things, an illumination system to produce a uniform intensity distribution of a received laser beam. It is desirable that the resulting illumination be as uniform as possible and that any uniformity errors be kept as small as possible. Illumination uniformity influences the ability of an illumination system to produce uniform line widths across an entire exposure field. Illumination uniformity errors can significantly impact the quality of devices produced by the lithography system.
One example of a popular conventional lithography system is a “step-and-scan” system. A “step-and-scan” system creates an illuminated slot narrower than one exposure field on the wafer. The system then scans this field along the fully exposure field and then steps to another field. This process is repeated. Because of the nature of the system's operation, radiation energy in the scan direction is integrated and as a result, can be non-uniform. However, the field must be uniform in the cross-scan direction. In other words, integrated energy along each scan line should remain the same.
In order to correct for uniformity errors, uniformity must be calculated, often in real-time. Uniformity is calculated as the ratio between the difference of the maximum and minimum value of the integral of the intensity in the cross scan (i.e., x) direction divided by the sum of the maximum and minimum value of the integral of the intensity. The integral of the intensity at each cross scan coordinate is given by a continuous triple integral equation including the product of transmissibility and “pupil” shape.
Finding a comprehensive way to express the product of the transmissibility and “pupil” shape as a function of the uniformity correction mechanism adds complexity. In addition, any algorithm that requires real-time computation of three integrals over every coordinate of interest is the illumination slot is not practical.
Therefore, a need exists for a uniformity correction system that can discretize the intensity integral.
A further need exists for a system that can determine and make adjustments to a correction system such that a defined uniformity specification is met while minimizing a set of selected constraints.